Capture-zone scaling in island nucleation: universal fluctuation behavior.

In island nucleation and growth, the distribution of capture zones (in essence proximity cells) can be described by a simple expression generalizing the Wigner surmise (power-law rise, Gaussian decay) from random matrix theory that accounts for spacing distributions in a host of fluctuation phenomena. Its single adjustable parameter, the power-law exponent, can be simply related to the critical nucleus of growth models and the substrate dimensionality. We compare with extensive published kinetic Monte Carlo data and limited experimental data. A phenomenological theory elucidates the result.

[1]  E. Placidi,et al.  Sudden nucleation versus scale invariance of InAs quantum dots on GaAs , 2007 .

[2]  A. Mount,et al.  Translocation of C60 and its derivatives across a lipid bilayer. , 2007, Nano letters.

[3]  T. Einstein Using the Wigner–Ibach surmise to analyze terrace-width distributions: history, user’s guide, and advances , 2006, cond-mat/0612311.

[4]  Y. Shim,et al.  Upper critical dimension for irreversible cluster nucleation and growth in the point-island regime. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  James W. Evans,et al.  Morphological evolution during epitaxial thin film growth: Formation of 2D islands and 3D mounds , 2006 .

[6]  T. Einstein,et al.  Evolution of terrace-width distributions on vicinal surfaces: Fokker-Planck derivation of the generalized Wigner surmise. , 2005, Physical review letters.

[7]  A. Abul-Magd Modelling gap-size distribution of parked cars using random-matrix theory , 2005, physics/0510136.

[8]  E. Placidi,et al.  How kinetics drives the two- to three-dimensional transition in semiconductor strained heterostructures: The case of InAs∕GaAs(001) , 2005, cond-mat/0510353.

[9]  Y. Shim,et al.  Island-size distribution and capture numbers in three-dimensional nucleation: Comparison with mean-field behavior , 2005 .

[10]  Frank Nüesch,et al.  Correlated growth in ultrathin pentacene films on silicon oxide: Effect of deposition rate , 2004 .

[11]  P. Mulheran The dynamics of island nucleation and growth—beyond mean-field theory , 2004 .

[12]  J. Amar,et al.  Asymptotic capture number and island size distributions for one-dimensional irreversible submonolayer growth , 2003, cond-mat/0307276.

[13]  M. Bartelt,et al.  Island sizes and capture zone areas in submonolayer deposition: Scaling and factorization of the joint probability distribution , 2002 .

[14]  F. Family,et al.  Rate-equation approach to island size distributions and capture numbers in submonolayer irreversible growth , 2001 .

[15]  V. Plerou,et al.  Random matrix approach to cross correlations in financial data. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  W. Steckelmacher Introduction to surface and thin film processes , 2001 .

[17]  M. Bartelt,et al.  Nucleation, adatom capture, and island size distributions: Unified scaling analysis for submonolayer deposition , 2001 .

[18]  P. Mulheran,et al.  Theory of the island and capture zone size distributions in thin film growth , 2000 .

[19]  T. Einstein,et al.  Implications of random-matrix theory for terrace-width distributions on vicinal surfaces : improved approximations and exact results , 1999 .

[20]  J. Villain,et al.  Physics of crystal growth , 1998 .

[21]  T. Guhr,et al.  RANDOM-MATRIX THEORIES IN QUANTUM PHYSICS : COMMON CONCEPTS , 1997, cond-mat/9707301.

[22]  Blackman,et al.  Scaling behavior in submonolayer film growth: A one-dimensional model. , 1996, Physical Review B (Condensed Matter).

[23]  Blackman,et al.  Capture zones and scaling in homogeneous thin-film growth. , 1996, Physical review. B, Condensed matter.

[24]  P. Mulheran,et al.  The origins of island size scaling in heterogeneous film growth , 1995 .

[25]  Amar Critical cluster size: Island morphology and size distribution in submonolayer epitaxial growth. , 1995, Physical review letters.

[26]  P. Mulheran On the statistical properties of the two-dimensional random voronoi network , 1992 .

[27]  Wolf,et al.  Surface diffusion and island density. , 1992, Physical review letters.

[28]  N. Bartelt,et al.  The influence of step-step interactions on step wandering , 1990 .

[29]  G. Le Caër,et al.  The Voronoi tessellation generated from eigenvalues of complex random matrices , 1990 .

[30]  Wertheim,et al.  Monte Carlo calculation of the size distribution of supported clusters. , 1989, Physical review. B, Condensed matter.

[31]  J. Wejchert,et al.  On the distribution of cell areas in a Voronoi network , 1986 .

[32]  B. Sutherland Quantum many body problem in one-dimension: Ground state , 1971 .

[33]  F. Calogero Solution of a three-body problem in one-dimension , 1969 .

[34]  F. Calogero Ground State of a One‐Dimensional N‐Body System , 1969 .

[35]  F. Haake Quantum signatures of chaos , 1991 .

[36]  F. Dyson Statistical Theory of the Energy Levels of Complex Systems. I , 1962 .